A loading apparatus and system is adapted to load unprocessed sample containers in a centrifuge and provide improved balance thereof. The apparatus has a staging platform containing at least two bucket inserts, a weight scale operable to determine a combined weight of each of the bucket inserts, a centrifuge configured to receive the bucket inserts as pairs, a robot operable to insert an unprocessed sample container into the bucket inserts, and a controller operable to command the robot to carry out placement of the unprocessed sample container into a highest priority empty receptacle of a lowest combined weight bucket insert. Methods of operating the system are provided.